Good Morning I have a Miele CV 4080. The waste that is discharged from the brewing unit to the waste container has become a runny mess recently, it used to discharge a solid pellet.

Have you changed your type of coffee beans or grind setting recently? First of all I would recommend removing and cleaning the brew unit thoroughly (as per cleaning instructions) to eliminate any cleaning issue here...
This is sounds like the flush valve is not working correctly. The flush valve ensures that all unused liquid in tubes is flushed into the driptray and that all solid coffee (dry pellet) goes from the brew chamber into the waste container. At the end of the coffee cycle when the pump stops running, the piston in the brew unit usually moves one last cycle and squeezes the coffee pellet in the chamber one last time and the flush valve operates so that all waste liquid is flushed from the coffee pellet to the drip tray. If your pellet is wet, then this final flush is not working. There may be a blockage in your flush tube or the flush valve may be blocked. These usually block up if you don't run a cleaning tablet through the machine regularly.
My advice is to remove the driptray grill and check that the tubes running into the tray from the brew unit are not accidentally squeezed closed or blocked. Good luck.